L2-STABILITY INDEPENDENT OF DIFFUSION FOR A FINITE ELEMENT-FINITE VOLUME DISCRETIZATION OF A LINEAR CONVECTION-DIFFUSION EQUATION

被引：12

作者：

Deuring, Paul ^{[1
,2
]}

Eymard, Robert ^{[3
]}

Mildner, Marcus ^{[1
,2
]}

机构：

[1] Univ Lille Nord France, F-59000 Lille, France

[2] ULCO, LMPA, F-62228 Calais, France

[3] Univ Paris Est Marne la Vallee, F-77454 Marne La Vallee, France

来源：

SIAM JOURNAL ON NUMERICAL ANALYSIS | 2015年 / 53卷 / 01期

关键词：

convection-diffusion equation; combined finite element-finite volume method; Crouzeix-Raviart finite elements; barycentric finite volumes; upwind method; stability; POINCARE-FRIEDRICHS INEQUALITIES; SCHEME; CONVERGENCE; STABILIZATION; FLOWS; H-1;

D O I：

10.1137/140961146

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We consider a time-dependent and a steady linear convection-diffusion equation. These equations are approximately solved by a combined finite element-finite volume method: the diffusion term is discretized by Crouzeix-Raviart piecewise linear finite elements on a triangular grid, and the convection term by upwind barycentric finite volumes. In the unsteady case, the implicit Euler method is used as time discretization. This scheme is shown to be unconditionally L-2-stable, uniformly with respect to the diffusion coefficient.

引用

页码：508 / 526

页数：19

共 50 条

[21] Finite volume methods for convection-diffusion problems
Lazarov, RD
Mishev, ID
Vassilevski, PS
SIAM JOURNAL ON NUMERICAL ANALYSIS, 1996, 33 (01) : 31 - 55
[22] The semidiscrete finite volume element method for nonlinear convection-diffusion problem
Zhang, Tong
APPLIED MATHEMATICS AND COMPUTATION, 2011, 217 (19) : 7546 - 7556
[23] Finite element methods for multicomponent convection-diffusion
Aznaran, Francis R. A.
Farrell, Patrick E.
Monroe, Charles W.
Van-Brunt, Alexander J.
IMA JOURNAL OF NUMERICAL ANALYSIS, 2024, 45 (01) : 188 - 222
[24] A Finite Volume Method for a Convection-Diffusion Equation Involving a Joule Term
Calgaro, Caterina
Creuse, Emmanuel
FINITE VOLUMES FOR COMPLEX APPLICATIONS IX-METHODS, THEORETICAL ASPECTS, EXAMPLES, FVCA 9, 2020, 323 : 405 - 413
[25] A weak Galerkin finite element method for nonlinear convection-diffusion equation
Li, Wenjuan
Gao, Fuzheng
Cui, Jintao
APPLIED MATHEMATICS AND COMPUTATION, 2024, 461
[26] Combined adaptive meshing technique and finite volume element method for solving convection-diffusion equation
Theeraek, Patcharee
Phongthanapanich, Sutthisak
Dechaumphai, Pramote
JAPAN JOURNAL OF INDUSTRIAL AND APPLIED MATHEMATICS, 2013, 30 (01) : 185 - 202
[27] Convergence rate of a finite volume scheme for the linear convection-diffusion equation on locally refined meshes
Coudière, Y
Villedieu, P
ESAIM-MATHEMATICAL MODELLING AND NUMERICAL ANALYSIS-MODELISATION MATHEMATIQUE ET ANALYSE NUMERIQUE, 2000, 34 (06): : 1123 - 1149
[28] Adaptive finite element for semi-linear convection-diffusion problems
Pouly, L
Pousin, J
ADVANCES IN COMPUTATIONAL MATHEMATICS, 1997, 7 (03) : 235 - 259
[29] On the convergence of a combined finite volume-finite element method for nonlinear convection-diffusion problems
Numer Methods Partial Differential Equations, 2 (163):
[30] Analysis of Linear Triangular Elements for Convection-diffusion Problems by Streamline Diffusion Finite Element Methods
ZHOU Jun-ming~1 JIN Da-yong~1 ZHANG Shu-hua~2 (1.Department of Mathematics
2.Department of Mathematics
数学季刊, 2007, (01) : 43 - 51

← 1 2 3 4 5 →